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Exercise:

Exercise 1

01. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
A. 1 year B. 2 years
C. 25 years D. Data inadequate
E. None of these

Answer and Explanation

Answer: Data inadequate

Explanation:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R - Q = ?.
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined. 

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02. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: 
A. 14 years B. 18 years
C. 20 years D. 22 years

Answer and Explanation

Answer: 22 years

Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.

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03. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: 
A. 14 years B. 19 years
C. 33 years D. 38 years

Answer and Explanation

Answer: 14 years

Explanation:
Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.

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04. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). 
A. 8, 20, 28 B. 16, 28, 36
C. 20, 35, 45 D. None of these

Answer and Explanation

Answer: 16, 28, 36

Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

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05. The ratio of the current ages of Ajay and Vijay is 7:4. The ratio between Ajay’s age 6 years ago and Vijay’s age 6 years from now is 1:1. Find the ratio between Ajay’s age 12 years hence and Vijay’s age 12 years ago.
A. 12:1 B. 10:1
C. 1:1 D. None of these

Answer and Explanation

Answer: 10:1

Explanation:
Let the current age of Ajay and Vijay be 7x and 4x respectively.
(7x – 6) / 4x + 6 = 1/1
7x – 6 = 4x + 6
3x = 12
x = 4
Therefore, (7x + 12) / (4x – 12) = (7*4 + 12) / (4 * 4 -12) = 40/4 = 10/1

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06. My father was 30 years of age when my sister was born. My mother was 38 years of age when I was born. My sister was 6 years of age when my brother was born who is 3 years elder to me. What was the age of my father and mother during the birth of my brother?
A. 41, 36 B. 24, 28
C. 28, 24 D. 36, 35

Answer and Explanation

Answer: 36, 35

Explanation:
My brother was born 6 years after my sister was born and 3 years before I was born.
Age of father during my brother’s birth = (30 + 6) = 36 years.
Age of mother during my brother’s birth = (38 – 3) = 35 years.
Hence, during the birth of my brother, my father was 36 years old and my mother was 35 years old.

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